Kirchhoff's voltage law (KVL)

Kirchhoff's voltage law says that if you walk all the way around any closed loop in a circuit and add up every voltage rise and drop, you arrive back where you started with a net change of zero. Think of hiking a loop trail: you go up and down hills, but when you return to the trailhead your total elevation change is exactly nothing. Voltage is electrical 'altitude', so a closed loop must sum to zero.

In symbols, the algebraic sum of voltages around a loop is zero: count a source as a rise and the drop across each resistor (I·R) as a fall, then balance them. This is conservation of energy for charge — moving a charge around a loop and back can't leave it with extra energy. KVL powers mesh analysis: write one voltage equation per loop and solve. For instance, in a 9 V battery driving two series resistors, the two resistor drops must add to exactly 9 V.